Dear NONMEM-Users,
I would like to raise a question which might be rather simple for experienced
users. However I didn't find the answer in the NONMEM user`s guide. Any help
would be highly appreciated.
That's the question:
Which degree of freedom must be used to compare the objective function if a
reduced model is compared with a full model and eliminated Thetas are related
to one variable?
NONMEM code (relevant part):
yyy1=0
yyy2=0
yyy3=0
yyy4=0
IF (yyy.EQ.1) yyy1=1
IF (yyy.EQ.2) yyy2=1
IF (yyy.EQ.3) yyy3=1
IF (yyy.EQ.4) yyy4=1
TEFF=TVBL*((SCORE1/3)**THETA(9))*(THETA(11)**yyy1)*(THETA(12)**yyy2)*(THETA(13)**yyy3)*(THETA(14)**yyy4)
In NONMEM user guide it is written that:
This statistic is approximately distributed chi-square (*2) with q degree of
freedom,
where q is the number of parameters whose values are fixed in the reduced
model. For
an *-level test, compare C2 to *1** 2 (q ), the 100(1-*) percentile of the *2
distribution.
In particular, when exactly one parameter of the full model is fixed in the
reduced model,
a decrease of 3.84 in the minimum value of the objective function is
significant at p<.05.
In this case since 4 Thetas are fixed in the reduced model, according to the
user guide, chi-square should be used to assess the level of significance with
a reduced degree of freedom of 4 (e.g. by function in excel)
However:
Although 4 thetas are estimated to describe the effect, the thetas will
influence only 1 parameter.
For each observation, one Theta is estimated whereas the rest is set to 0 (see
code above), therefore I am not certain if I should use a degree of freedom
reduced by 1 or by 4 to compare both models.
Many thanks on advance
Dirk
Dirk Garmann, PhD
Clinical Scientific Expert /Pharmacokineticist
Merz Pharmaceuticals
Clinical Pharmacology
Eckenheimer Landstrasse 100
60318 Frankfurt
Phone +49 (69) 1503 720
Merz Pharmaceuticals GmbH, Frankfurt am Main
Amtsgericht Frankfurt am Main, HRB 53808
Geschäftsführung: Dr. Martin Zügel (Vors.), Dr. Alexander Gebauer, Dr. Eugen
Wilbert
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Charakter. Dies ist kein Anerkenntnis, dass es sich beim Inhalt dieser E-Mail
um eine rechtsverbindliche Erklärung der entsprechenden Gesellschaft der Merz
Gruppe handelt, es sei denn dies ist ausdrücklich als solches formuliert.
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AW: CompareModels
Dear Dirk,
If your full model has 4 parameters more than your reduced model, and you
estimate all four of them, it does not matter how many observations
contribute to each of them. Thus you should evaluate Diff_OFV at 4 degrees
of freedom.
Happy modelling,
Joachim
Joachim Grevel, PhD
Scientific Director
BAST Inc Limited
BioCity Nottingham
Pennyfoot Street
Nottingham, NG1 1GF
Tel: +44 (0)115 8120497
Quoted reply history
From: [email protected] [mailto:[email protected]] On
Behalf Of Garmann, Dirk
Sent: 18 January 2011 13:07
To: [email protected]
Subject: [NMusers] AW: CompareModels
Dear NONMEM-Users,
I would like to raise a question which might be rather simple for
experienced users. However I didnt find the answer in the NONMEM user`s
guide. Any help would be highly appreciated.
Thats the question:
Which degree of freedom must be used to compare the objective function if a
reduced model is compared with a full model and eliminated Thetas are
related to one variable?
NONMEM code (relevant part):
yyy1=0
yyy2=0
yyy3=0
yyy4=0
IF (yyy.EQ.1) yyy1=1
IF (yyy.EQ.2) yyy2=1
IF (yyy.EQ.3) yyy3=1
IF (yyy.EQ.4) yyy4=1
TEFF=TVBL*((SCORE1/3)**THETA(9))*(THETA(11)**yyy1)*(THETA(12)**yyy2)*(THETA(
13)**yyy3)*(THETA(14)**yyy4)
In NONMEM user guide it is written that:
This statistic is approximately distributed chi-square (c2) with q degree of
freedom,
where q is the number of parameters whose values are fixed in the reduced
model. For
an a-level test, compare C2 to c1-a 2 (q ), the 100(1-a) percentile of the
c2 distribution.
In particular, when exactly one parameter of the full model is fixed in the
reduced model,
a decrease of 3.84 in the minimum value of the objective function is
significant at p<.05.
In this case since 4 Thetas are fixed in the reduced model, according to the
user guide, chi-square should be used to assess the level of significance
with a reduced degree of freedom of 4 (e.g. by function in excel)
However:
Although 4 thetas are estimated to describe the effect, the thetas will
influence only 1 parameter.
For each observation, one Theta is estimated whereas the rest is set to 0
(see code above), therefore I am not certain if I should use a degree of
freedom reduced by 1 or by 4 to compare both models.
Many thanks on advance
Dirk
Dirk Garmann, PhD
Clinical Scientific Expert /Pharmacokineticist
Merz Pharmaceuticals
Clinical Pharmacology
Eckenheimer Landstrasse 100
60318 Frankfurt
Phone +49 (69) 1503 720
_____
Merz Pharmaceuticals GmbH, Frankfurt am Main
Amtsgericht Frankfurt am Main, HRB 53808
Geschäftsführung: Dr. Martin Zügel (Vors.), Dr. Alexander Gebauer, Dr. Eugen
Wilbert
_____
Die vorgenannten Angaben der E-Mail haben grundsätzlich nur informativen
Charakter. Dies ist kein Anerkenntnis, dass es sich beim Inhalt dieser
E-Mail um eine rechtsverbindliche Erklärung der entsprechenden Gesellschaft
der Merz Gruppe handelt, es sei denn dies ist ausdrücklich als solches
formuliert. Erklärungen, die eine Gesellschaft der Merz Gruppe verpflichten
sollen, bedürfen jeweils der Unterschrift durch zwei zeichnungsberechtigte
Personen dieser Gesellschaft.
Diese E-Mail enthält vertrauliche und/oder rechtlich geschützte
Informationen. Wenn Sie nicht der richtige Adressat sind oder diese E-Mail
irrtümlich erhalten haben, informieren Sie bitte sofort den Absender und
vernichten Sie diese E-Mail. Das unerlaubte Kopieren sowie die unbefugte
Weitergabe dieser E-Mail ist nicht gestattet.